Question

The point (1, –3), (13, 9), (10, 12) and (–2, 0) taken in order form the vertices of _________________

• A. Square
• B. Rectangle
• C. Rhombus
• D. Triangle

Answer 1

The correct option is B Rectangle

Let's name the points as A (1, –3), B(13, 9), C(10, 12) and D(–2, 0)

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$

$=\sqrt{(x_2-x_1{)}^2-(y_2-y_1{)}^2}$

$A{B}^2=(13-1{)}^2+(9+3{)}^2$
= 144 + 144
= 288
AB = $\sqrt{288}$ units

$B{C}^2=(10-13{)}^2+(12-9{)}^2$
= 9 + 9
= 18
BC = $\sqrt{18}$ units

$C{D}^2=(-2-10{)}^2+(0-12{)}^2$
= 144 + 144
= 288
CD = $\sqrt{288}$ units

$D{A}^2=(1+2{)}^2+(-3-0{)}^2$
= 9 + 9
= 18
DA = $\sqrt{18}$ units

Since opposite sides are equal, from the given options we can say that the figure is a rectangle.